Coplanar Newtonian models with outer periods of 1,507 and 4,500 days fit nine TOI-4562 b transit times

We test whether nine public transit times of TOI-4562 b select a single outer orbit. Seven times come from Fermiano et al. (2024). Two 2025 times come from SCI publication 06226c83-57d2-45f0-94a4-b32dfde8aaa9. We construct two coplanar Newtonian models with outer periods of 1,507.08 and 4,500.00 days. The outer masses are 0.563 and 4.578 Jupiter masses. With seven free parameters, their chi-square values are 3.110 and 2.953. A constant-period fit gives 2,538.74. We fix the stellar mass, inner planet mass, inner eccentricity, and orbit planes. An independent direct integration agrees with the transit calculation to less than 0.0001 second through cycle 26. Both examples remain bound at sampled times in 10,000-year Newtonian checks. Their predictions differ by 4.30 minutes in December 2026 and 101.18 minutes in July 2027. Prior work already showed ambiguity with seven times and reported later short-period alternatives. This contribution supplies explicit short- and long-period examples for nine tabulated times, full initial states, and later predictions. The 4,500-day period is at a search bound and is not a period estimate. We do not fit all available observations, radial velocities, or transit durations. These examples do not establish a new planet, posterior probabilities, or stability over the system age. The package preserves source data, provenance, completed searches, code, solver checks, results, figures, and reproduction instructions.

TOI-4562 b · transit timing variations · orbital degeneracy · Newtonian dynamics · TESS · reproducible astronomy